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Expand and simplify (x+3)(x + 5)

Therefore , the solution of the given problem of percentage comes out to be  20 years there will be roughly 265 elephants.

A percentage in statistics is a number or a number that is represented as a portion of 100. Additionally, "pct.," "pct," and "pc" are infrequently employed. However, the "%" symbol is frequently used to indicate it. The percentage sum is flat; there are no dimensions. Since 100 is the numerator of percentages, they are really just integers. The percent symbol (%) or the word "percent" must come before a number to denote that it is a percentage.

Here,

Elephant population after each year is 97% of the population after the preceding year if the population is declining at a rate of 3% per year.

We can use the following equation to determine the number of elephants in 20 years:

Population after 20 years is equal to the initial population multiplied by (1 - rate of decline/100) years.

Inputting the numbers provided yields:

=> 20-year population = 486 * (1 - 3/100)

=> 20 People after 20 years= 486*0.97.

=> 20 Years Later, Number = 486 x 0.5459

=> 20 years later, the population is 265,26.

Consequently, in 20 years there will be roughly 265 elephants.

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The quadratic equation x^2 - 3kx - 4k^2 = 0 will have real-valued solutions for values of k such that the discriminant (b^2 - 4ac) is greater than or equal to zero.

The given quadratic equation is x^2 - 3kx - 4k^2 = 0.

Comparing this equation with the standard form ax^2 + bx + c = 0, we have:

a = 1, b = -3k, and c = -4k^2.

The discriminant is given by b^2 - 4ac. Substituting the values, we get:

(-3k)^2 - 4(1)(-4k^2) = 9k^2 + 16k^2 = 25k^2.

For real-valued solutions, the discriminant should be greater than or equal to zero: 25k^2 ≥ 0.

To find the values of k for which the quadratic equation has real-valued solutions, we need to solve the inequality 25k^2 ≥ 0.

Since the square of any real number is non-negative, the inequality is satisfied for all real values of k. Therefore, the quadratic equation x^2 - 3kx - 4k^2 = 0 will have real-valued solutions for all values of k.

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Answer:

p = -3

Step-by-step explanation:

-2 = p - 1

+1       +1

-1 = p

Answer:

Look in the explanation

Step-by-step explanation:

Add 1 to each side

-2+1=p-1+1

-1=p

p=-1

The upper bound of the 95% confidence interval for the average age in the U.S. is 48.29 years.

To determine the upper bound of the 95% confidence interval for the average age in the U.S., we can use the sample data from the survey. The sample size is 1072 people, randomly selected from the U.S. population, with a minimum age of 12. By calculating the average age of the respondents, we can estimate the average age of the entire U.S. population.

Using the given information that the average age of the respondents is 43.56 years, and assuming that the sample is representative of the population, we can calculate the standard error. The standard error measures the variability of the sample mean and indicates how much the sample mean might deviate from the population mean.

Using statistical methods, we can calculate the standard error and construct a confidence interval around the sample mean. The upper bound of the 95% confidence interval represents the highest plausible value for the population average age based on the sample data.

Therefore, based on the provided information and calculations, the upper bound of the 95% confidence interval for the average age in the U.S. is 48.29 years.

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Many children develop the ability to do simple arithmetic problems during their early childhood years, typically between the ages of 4 and 6. Correct option is a).

During this time, children start to understand basic mathematical concepts such as counting, addition, and subtraction. They may also begin to recognize and name numbers and use basic math vocabulary. However, it's important to note that every child develops at their own pace and some may show these skills earlier or later than others. It's also important for parents and caregivers to provide opportunities for children to practice and reinforce these skills through activities such as counting objects, playing number games, and solving simple math problems.

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The simplified expression for (f ∘ g)(x) is 2 + x (option d).

To find and simplify (f ∘ g)(x), we need to substitute the expression for g(x) into f(x) and simplify.

Given:

f(x) = log₃(9x)

g(x) = \(3^x\)

Substituting g(x) into f(x):

(f ∘ g)(x) = f(g(x)) = log₃\((9 * 3^x)\)

Now, we simplify the expression:

log₃\((9 * 3^x)\) = log₃(9) + log₃\((3^x)\)

Since logₓ(a * b) = logₓ(a) + logₓ(b), we have:

log₃(9) + log₃\((3^x)\) = log₃\((3^2)\) + x

Using the property logₓ\((x^a)\) = a * logₓ(x), we get:

log₃\((3^2)\) + x = 2 * log₃(3) + x

Since logₓ\((x^a)\) = a, where x is the base, we have:

2 * log₃(3) + x = 2 + x

Therefore, (f ∘ g)(x) simplifies to:

(f ∘ g)(x) = 2 + x

So, the correct answer is (d) 2 + x.

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Complete Question:

Given f(x)=log₃(9x) and g(x)=\(3^x\). Find and simplify (f ∘ g)(x)

(a) 2x

(b) x

(c) \(27^x\)

(d) 2+x

(e) None of these.

The type i error- That means rejecting the null hypothesis when the mean price of mid-sized cars is $32000

type 2 error- That means accepting the null hypothesis when the mean price of mid-sized cars is not $32000

What are type i and type ii errors?

Type one error means rejecting the null hypothesis when actually it is true. And type 2 error means accepting null hypothesis when actually it is false.

We are given, the mean price (population mean) of mid-sized cars in a region is $32,000.

Also a test is conducted to see if the claim is true or not

The null hypothesis can be given as the mean price of mid-sized cars in a region is $32000.

The type 1 error can be given as rejecting the null hypothesis when it is true

That means rejecting the null hypothesis when the mean price of mid-sized cars is $32000

The type 2 error can be given as accepting the null hypothesis when it is false

That means  the accepting null hypothesis when the mean price of mid-sized cars is not $32000

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Answer:

262.44 cubic metres.

Step-by-step explanation:

First, we can calculate the volume of the cylinder by doing pi * r^2 * h. In this case, r is 5 / 2 and h is 7.

pi * (5/2)^2 * 7 = pi * 25/4 * 7 = pi * 6.25 * 7 = pi * 43.75 = 3.14159265 * 43.75 = 137.4446784 cubic m.

Seconds, we calculate the volume of the cube. It is 5^3 = 5 * 5 * 5 = 25 * 5 = 125 cubic m.

137.4446784 + 125 = 262.4446784, which is about 262.44 cubic metres.

Hope this helps!

Answer:

5*5*5=125

volume of cylinder=137.44

137.44+125=262.44

Step-by-step explanation:

Answer:
The fox is faster, by 7 miles per hour

Step-by-step explanation:

The fox can run 21 miles in half an hour -> It can run 42 miles in an hour

And the rabbit can run 35 miles per hour, so the fox run fastest by 42-35 = 7(m/h)

Answer:

the fox can run faster by 17 mph!

Step by step explanation:

This problem involves ratios

Our two ratios involve the distance the animals ran (the 35 & 21) and the time it took for them to run that distance (the 1 & 0.5)

So our two ratios are 1:35 (it took the rabbit 1 hour to run 35 miles) and 0.5:21 (it took the fox half an hour to run 21 miles)

But before we start subtracting, we have to take into account the fact that the time periods are not the same!

To start subtracting, we need to 0.5 and 1 to be the same or vice versa, the 1 to be a 0.5

In this case, let’s make the 0.5:21 bigger because it’s often easier to multiply than divide

When we multiply 0.5 by 2, it gets us to 1 so we have to do the same to the 21.

21x2=42

So our new ratio is 1:42

Now we can directly compare the two ratios.

42-35=17

So the fox ran faster by 17 miles

PLEASE AWARD BRAINLIEST I NEED TO LEVEL UP!

To rewrite the linear system as a matrix equation, we can let y = [y1, y2, y3] and A be the coefficient matrix:

y' = Ay
where
A = [1 1 2; 1 0 1; 2 1 3]

To compute the eigenvalues of A, we can use the formula:
det(A - λI) = 0
where det represents the determinant and I is the identity matrix.

So, we have:
|1-λ 1 2|     |1 1-λ 2|     |1 1 1-λ|
|1 0-λ 1|  =  |1 0 1|  =  |1-λ 0 1|
|2 1 3-λ|     |2 1 3|     |2 1 3-λ|

Expanding the determinants, we get:
(1-λ)[(0-λ)(3-λ)-1]-1[(1)(3-λ)-2(1)]+2[(1)(1)-2(1-λ)]
= (λ-3)(λ-1)(λ-2) = 0

Therefore, the eigenvalues of A are 3, 1, and 2.

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1. The parametric equation of the line passing through the points (x+6, y-3) and (2, -3) can be found by subtracting the coordinates of the two points and expressing the equations in terms of a parameter t.

2. The z-intercept of the plane given by the equation (x, y, z) = (4, 6, 5) + s(2, 3, 1) + t(3, 6, 12) can be found by substituting x = 0 and y = 0 into the equation and solving for z.

1. To find the parametric equation of the line, we subtract the coordinates of the two points: (x+6, y-3) - (2, -3). This gives us the direction vector of the line. We then express the equations in terms of a parameter t to obtain the parametric equations for x and y.

2. To find the z-intercept of the plane, we substitute x = 0 and y = 0 into the equation (x, y, z) = (4, 6, 5) + s(2, 3, 1) + t(3, 6, 12). This simplifies the equation to z = 5 + s + 2t. Since we are looking for the z-intercept, we set x = 0 and y = 0, and solve for z. The resulting value of z gives us the coordinates of the z-intercept.

3a. To determine the Cartesian equation of the plane with x, y, and z-intercepts at -2, 4, and -3 respectively, we can use the intercept form of the equation of a plane, which states that (x/a) + (y/b) + (z/c) = 1, where a, b, and c are the intercepts. Substituting the given values, we obtain the Cartesian equation of the plane.

3b. The Cartesian equation of the plane that passes through the origin and is parallel to the plane in part a can be obtained by shifting the intercepts by the corresponding amount. Since the plane passes through the origin, the intercepts remain the same, resulting in the Cartesian equation of the parallel plane.

3c. The vector equation of the line of intersection between the plane in part b and the xy-plane can be found by setting z = 0 in the Cartesian equation of the plane. This simplifies the equation to an equation involving x and y, representing the line of intersection in vector form.

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Answer:

it equals 44,693.81

Step-by-step explanation:

hope it helps you:)

Answer:

44,693.81

Step-by-step explanation:

bc its right i used a calculator

1. The solution to the first differential equation is given by e^2yx - ysin(xy) + y^2 + C = 0, where C is an arbitrary constant.

2. The general solution to the second differential equation is x(3x - y^2) = C, where C is a positive constant.

To solve the first-order differential equations, let's solve them one by one:

1. (e^2y - ycos(xy))dx + (2xe^2y - xcos(xy) + 2y)dy = 0

We notice that the given equation is not in standard form, so let's rearrange it:

(e^2y - ycos(xy))dx + (2xe^2y - xcos(xy))dy + 2ydy = 0

Comparing this with the standard form: P(x, y)dx + Q(x, y)dy = 0, we have:

P(x, y) = e^2y - ycos(xy)

Q(x, y) = 2xe^2y - xcos(xy) + 2y

To check if this equation is exact, we can compute the partial derivatives:

∂P/∂y = 2e^2y - xcos(xy) - sin(xy)

∂Q/∂x = 2e^2y - xcos(xy) - sin(xy)

Since ∂P/∂y = ∂Q/∂x, the equation is exact.

Now, we need to find a function f(x, y) such that ∂f/∂x = P(x, y) and ∂f/∂y = Q(x, y).

Integrating P(x, y) with respect to x, treating y as a constant:

f(x, y) = ∫(e^2y - ycos(xy))dx = e^2yx - y∫cos(xy)dx = e^2yx - ysin(xy) + g(y)

Here, g(y) is an arbitrary function of y since we treated it as a constant while integrating with respect to x.

Now, differentiate f(x, y) with respect to y to find Q(x, y):

∂f/∂y = e^2x - xcos(xy) + g'(y) = Q(x, y)

Comparing the coefficients of Q(x, y), we have:

g'(y) = 2y

Integrating g'(y) with respect to y, we get:

g(y) = y^2 + C

Therefore, f(x, y) = e^2yx - ysin(xy) + y^2 + C.

The general solution to the given differential equation is:

e^2yx - ysin(xy) + y^2 + C = 0, where C is an arbitrary constant.

2. x(yy' - 3) + y^2 = 0

Let's rearrange the equation:

xyy' + y^2 - 3x = 0

To solve this equation, we'll use the substitution u = y^2, which gives du/dx = 2yy'.

Substituting these values in the equation, we have:

x(du/dx) + u - 3x = 0

Now, let's rearrange the equation:

x du/dx = 3x - u

Dividing both sides by x(3x - u), we get:

du/(3x - u) = dx/x

To integrate both sides, we use the substitution v = 3x - u, which gives dv/dx = -du/dx.

Substituting these values, we have:

-dv/v = dx/x

Integrating both sides:

-ln|v| = ln|x| + c₁

Simplifying:

ln|v| = -ln|x| + c₁

ln|x| + ln|v| = c₁

ln

|xv| = c₁

Now, substitute back v = 3x - u:

ln|x(3x - u)| = c₁

Since v = 3x - u and u = y^2, we have:

ln|x(3x - y^2)| = c₁

Taking the exponential of both sides:

x(3x - y^2) = e^(c₁)

x(3x - y^2) = C, where C = e^(c₁) is a positive constant.

This is the general solution to the given differential equation.

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Answer:

7 traders sell oranges and mangoes alone.

Step-by-step explanation:

(21 + 4 + 5 + 10 + x + 35 – x + 32 – x = 100)

(107 – x = 100)

(x = 107 – 100 = 7)

Therefore, 7 traders sell oranges and mangoes alone.

(b) (312_{four} + 52_{x} = 96_{ten})

(312_{4} = 3 times 4^{2} + 1 times 4^{1} + 2 times 4^{0})

= (48 + 4 + 2 = 54_{10})

(52_{x} = 5 times x^{1} + 2 times x^{0})

= ((5x + 2)_{10})

(therefore 54 + (5x + 2) = 96)

(56 + 5x = 96 implies 5x = 96 – 56 = 40)

(x = 8)

(therefore 312_{4} + 52_{8} = 96_{10})

Answer:

1 → e

2 → f

3 → b

4 → d

5 → a

Step-by-step explanation:

Look for the corresponding sides by paying attention to the angle pairs since the angles do not change when the polygon is scaled.

Question 1a

To calculate the book value at the end of the first year using straight-line depreciation, we need to determine the annual depreciation expense first. The straight-line method assumes that the asset depreciates by an equal amount each year over its useful life. Therefore, we can use the following formula to calculate the annual depreciation:

Annual Depreciation = (Cost - Salvage Value) / Useful Life

Substituting the given values, we get:

Annual Depreciation = ($200,000 - $20,000) / 10 years = $18,000 per year

This means that the tractor will depreciate by $18,000 each year for the next 10 years.

To determine the book value at the end of the first year, we need to subtract the depreciation expense for the year from the original cost of the tractor. Since one year has passed, the depreciation expense for the first year will be:

Depreciation Expense for Year 1 = $18,000

Therefore, the book value of the tractor at the end of the first year will be:

Book Value = Cost - Depreciation Expense for Year 1

= $200,000 - $18,000

= $182,000

So the book value of the tractor at the end of the first year, December 31, 2022, using straight-line depreciation is $182,000. so the answer is D

Question 1(b)

To determine the farmer's noncurrent liabilities, we need to use the information provided to calculate the total liabilities and then subtract the current liabilities from it. Here's the step-by-step solution:

Calculate the total current liabilities using the current ratio:

Current Ratio = Current Assets / Current Liabilities

2 = $80,000 / Current Liabilities

Current Liabilities = $80,000 / 2

Current Liabilities = $40,000

Calculate the total liabilities using the debt/equity ratio:

Debt/Equity Ratio = Total Liabilities / Owner Equity

1.0 = Total Liabilities / $100,000

Total Liabilities = $100,000 * 1.0

Total Liabilities = $100,000

Subtract the current liabilities from the total liabilities to get the noncurrent liabilities:

Noncurrent Liabilities = Total Liabilities - Current Liabilities

Noncurrent Liabilities = $100,000 - $40,000

Noncurrent Liabilities = $60,000

Therefore, the farmer's noncurrent liabilities are $60,000. so the answer is B.

Answer:

3

Step-by-step explanation:

Answer:

19

Step-by-step explanation:

Answer:

19

Step-by-step explanation:

9+10=19.

Add 9 to 10.

It's 19.

Man, that's so hard!
Even I had to use a calculator.

Answer:

13

Step-by-step explanation:

1+1=2

1+2=3

2+3=5

3+5=8

8+blank=21

21-8=13

Answer:

13

1+1=2+3=5+8=13+21=...

The function that represents the vertical stretch by a factor of 3 of f(x) is given as follows:

g(x) = 3x - 21.

Vertical stretches or compression to the graph of a function f(x) are applied by the multiplication of a constant a to the function, as follows:

g(x) = a x f(x).

Then the value of the constant determines if it is an stretch or a compression.

For this problem, we want a vertical stretch with a factor of 3, then the constant is given as follows:

a = 3.

Then the definition of function g(x) is given by:

g(x) = 3f(x)

g(x) = 3(x - 7)

g(x) = 3x - 21.

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Answer:

157m

Step-by-step explanation:

*see image for diagram

cos 27 = \(\frac{x}{176m}\)

x = 176*cos27

x = 156.8171...

Answer:

the answer is 157 m explained in detail above

Answer:

Explanation:

Here, we want to write the equation of the quadratic function

We have the general form as:

from the question, we have the horizontal intercepts at t= 3 and t =4

that means (t-3) is a factor and also (t-4) is another root of the equation

The product of these two is as follows:

Finally, we need to find the value of a

We can do this by making a substitution

We substitute 1 for t and -3 on the other side of the equation

Mathematically, we have this as:

Thus, we have the equation as:

The confidence interval constructed in part (a) would still be valid, regardless of the normality assumption.

(A) Using the given information, a 99.9% confidence interval for the population mean is calculated as [35.28, 40.66] rounded to at least two decimal places.

(B) If the population is not approximately normal, the validity of the confidence interval constructed in part (a) may be compromised. However, since the sample size (n=62) is sufficiently large, the central limit theorem can be applied, allowing for the use of a z-distribution and resulting in a valid confidence interval.

Therefore, the confidence interval constructed in part (a) would still be valid, regardless of the normality assumption.

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Answer:

D

Step-by-step explanation:

x^2 - 4x + 4 = 36

Take the square root on both sides.

x - 2x + 2 = 6

Answer:

Bottom right on TTM/Imagine Math    on the question asked it is d.

Step-by-step explanation:

We can use a statistical approach. First, we can calculate the proportion of visitors who purchased exactly one costume on the given day:

51/(6+51+6) = 0.81

This means that about 81% of the visitors purchased exactly one costume. To estimate how many visitors out of 200 would buy exactly one costume, we can multiply the proportion by the total number of visitors:

0.81 * 200 = 162

Therefore, we would expect around 162 visitors to buy exactly one costume next week. However, it's important to note that this is only an estimate based on the given data, and there may be other factors that could affect the actual number of purchases. Additionally, rounding the answer to the nearest whole number may introduce some error, so it's important to keep in mind that the actual number could be slightly higher or lower.

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(1). Eighteen minus a number: 18 - x. (2). A quantity less five: y - 5 (3). Four times a number is sixteen: 4z = 16 (4). Five times a number is two more than twice that number: 5w = 2 + 2w (5). Twelve more than a number: v + 12

1. Eighteen minus a number:

Let the number be represented by the variable "x".

The mathematical expression would be: 18 - x.

2. A quantity less five:

Let the quantity be represented by the variable "y".

The mathematical expression would be: y - 5.

3. Four times a number is sixteen:

Let the number be represented by the variable "z".

The mathematical expression would be: 4z = 16.

4. Five times a number is two more than twice that number:

Let the number be represented by the variable "w".

The mathematical expression would be: 5w = 2 + 2w.

5. Twelve more than a number:

Let the number be represented by the variable "v".

The mathematical expression would be: v + 12.

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Answer:

x = 9

Step-by-step explanation:

8 = 12k  Divide both sides by 12

k = 2/3

6 = 2/3 x  Multiply both sides by 3/2

x = 9

The TRUE statements are:

A row replacement operation does not affect the determinant of a matrix.

(a) A row interchange operation changes the sign of the determinant of a matrix. Therefore, statement (a) is false.

(b) A row replacement operation corresponds to multiplying the determinant by a scalar, so it does not change the determinant itself. Therefore, statement (b) is true.

(c) The determinant of the sum of two matrices is not in general equal to the sum of the determinants of the individual matrices. Therefore, statement (c) is false.

(d) The determinant of the given matrix is given by:

\($\begin{vmatrix}a&0&0\b&c&0\d&e&f\end{vmatrix} = a\begin{vmatrix}c&0\e&f\end{vmatrix} - b\begin{vmatrix}0&0\d&f\end{vmatrix} + d\begin{vmatrix}0&c\e&f\end{vmatrix}$\)

Simplifying each 2x2 determinant:

\($\begin{vmatrix}c&0\e&f\end{vmatrix} = cf$\)

\($\begin{vmatrix}0&0\d&f\end{vmatrix} = 0$\)

\($\begin{vmatrix}0&c\e&f\end{vmatrix} = -ce$\)

Substituting back into the original expression:

\($a(cf) - b(0) + d(-ce) = acf - cde$\)

Therefore, statement (d) is true.

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The solution of the system of equation is x = -1 and y=10/3.

The correct option is A.

Given

The given system of equation is;

\(\rm x + 3y = 9\\\\3x - 3y = -13\)

A system of linear equations is a collection of two or more linear equations.

From equation 1

\(\rm x+3y=9\\\\x=9-3y\)

Substitute the value of x in equation 2

\(\rm 3x-3y=-13\\\\3(9-3y)-3y=-13\\\\27-9y-3y=-13\\\\-12y=-13-27\\\\-12y=-40\\\\12y=40\\\\y = \dfrac{40}{12}\\\\y=\dfrac{10}{3}\)

Substitute the value of y in equation 1

\(\rm x+3y=9\\\\ x + 3\dfrac{10}{3}=9\\\\x+10=9\\\\x=9-10\\\\x=-1\)

Hence, the solution of the system of equation is x = -1 and y=10/3.

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Answer:

A

Step-by-step explanation:

The exponential probability density function is a continuous probability distribution that models the time between independent events occurring at a constant rate. The formula for P(x ≤ x0) is given by Formula #1, which is the cumulative distribution function (CDF) for the exponential distribution.

To calculate the probabilities, we can use the formula P(x ≤ x0) = 1 - e^(-λx0), where λ is the rate parameter and x0 is the value of interest.

Using this formula, we can find P(x ≤ 2) = 0.3935, P(x ≥ 3) = 0.0498, P(x ≤ 6) = 0.9179, and P(2 ≤ x ≤ 6) = 0.5242, all to 4 decimal places.

It is important to note that the exponential distribution has the memoryless property, meaning that the probability of an event occurring in the next time interval is independent of the length of time since the previous event.

This property makes the exponential distribution useful in many real-world applications, such as queuing theory and reliability analysis.

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